Lecture 8. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 8 – Tuesday 2/5/2013. Block 1: Mole Balances Block 2: Rate Laws Block 3: Stoichiometry
Lecture 8 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.
Lecture 8 – Tuesday 2/5/2013 • Block 1: Mole Balances • Block 2: Rate Laws • Block 3: Stoichiometry • Block 4: Combine • Pressure Drop • Liquid Phase Reactions • Gas Phase Reactions • Engineering Analysis of Pressure Drop
Pressure Drop in PBRs Concentration Flow System: Gas Phase Flow System:
Pressure Drop in PBRs Note: Pressure Drop does NOT affect liquid phase reactions Sample Question: Analyze the following second order gas phase reaction that occurs isothermally in a PBR: AB Mole Balances Must use the differential form of the mole balance to separate variables: Rate Laws Second order in A and irreversible:
Pressure Drop in PBRs Stoichiometry Isothermal, T=T0 Combine: Need to find (P/P0) as a function of W (or V if you have a PFR)
Pressure Drop in PBRs ErgunEquation: Constant mass flow:
Pressure Drop in PBRs Variable Density Let
Pressure Drop in PBRs Where CatalystWeight Let
Pressure Drop in PBRs Wewilluse this form for singlereactions: Isothermal case
Pressure Drop in PBRs and or The two expressions are coupledordinary differential equations. Wecanonlysolvethemsimultaneouslyusing an ODE solversuch as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution. Polymath will combine the Mole Balances, Rate Laws and Stoichiometry.
Pressure Drop in a PBR 1 P W
Reaction Rate in a PBR 3 -rA W
Conversion in a PBR 4 X W
Flow Rate in a PBR 5 1 W
Example 1:Gas Phase Reaction in PBR for δ=0 Gas Phase reaction in PBR with δ = 0 (Analytical Solution) A + B 2C Repeat the previous one with equimolar feed of A and B and: kA = 1.5dm6/mol/kg/min α = 0.0099 kg-1 Find X at 100 kg
Example 1:Gas Phase Reaction in PBR for δ=0 1) Mole Balance 2) Rate Law 3) Stoichiometry
Example 1:Gas Phase Reaction in PBR for δ=0 , , 4) Combine
Example 2:Gas Phase Reaction in PBR for δ≠0 The reaction A + 2B C is carried out in a packed bed reactor in which there is pressure drop. The feed is stoichiometric in A and B. Plot the conversion and pressure ratio y = P/P0 as a function of catalyst weight up to 100 kg. Additional Information kA = 6 dm9/mol2/kg/min α = 0.02 kg-1
Example 2:Gas Phase Reaction in PBR for δ≠0 A + 2B C 3) Stoichiometry: Gas, Isothermal 1) Mole Balance 2) Rate Law
Example 2:Gas Phase Reaction in PBR for δ≠0 4) 7) 6) 5) Initial values: W=0, X=0, y=1 Final values: W=100 Combine with Polymath. If δ≠0, polymath must be used to solve.
Robert the Worrier wonders: What if we increase the catalyst size by a factor of 2?
Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance
Pressure Drop - Summary • Pressure Drop • Liquid Phase Reactions • Pressure Drop does not affect concentrations in lquid phase reactions. • Gas Phase Reactions • Epsilon does not equal to zero d(P)/d(W)=… Polymath will combine with d(X)/d(W) =… for you • Epsilon = 0 and isothermal P=f(W) Combine then separate variables (X,W) and integrate • Engineering Analysis of Pressure Drop
Pressure Change – Molar Flow Rate Use for heat effects, multiple rxns Isothermal: T = T0
Example 1:Gas Phase Reaction in PBR for δ=0 A + B 2C Case 1: Case 2: